Radiation is by far the slowest means to transfer heat.
So, if you were in a vacuum, you’d lose heat surprisingly slowly even if the outside temperature was near absoluter zero.
If I put you in a bath of liquid nitrogen things would be different. Now we are into conduction. This is a LOT faster.
How fast would you die in it though? I have no idea. You’d suffer severe injury immediately but I suspect it’d take awhile for you to expire this way (although you’d probably be terminal real fast). Your outside would freeze but your core would take a lot longer to freeze…particularly since you’d be generating heat.
The question though, as asked, posited an absence of things. An absence of heat, to me, is not a bath of liquid nitrogen…it is nothing (think of something like deep space…I know it is not absolute zero but near enough for this). In that case the absence of heat is the least of your worries. Heck, the Space Shuttle had more problems cooling itself than it did staying warm in space (its electronics and people heated the environment and they had to work to get rid of the heat).